You really should first check that the tree doesn't have a TPO attached to it. If it does, you really must apply to the local planning authority for permission to prune, even if it is overhanging your garden. We have currently had a problem where someone has physically ripped branches from our protected Copper Beech, which was overhanging the road above a 6' fence. The fine, for damaging a tree in a manner likely to destroy it, is £20,000 and you could still be fined a few thousand for pruning without permission. If in doubt, check!